Orthogonal harmonic polynomials onU(2)

Electric charges and free electromagnetic waves are supposed to be described locally with the same wave differential equation. It is only the topology that is considered to be different. The calculated nonlocalU(2) individuals are characterized by polynomials that belong neither to the classical nor to the Szegö polynomials. The construction of the polynomial solution in component form, their orthogonality over singular measures, the relationships to the Jacobi polynomials, Rodriguez formulas, product decomposition, asymptotic formulas, and completeness are presented in some detail. The possibility is discussed of whether this highly nonlocal model for electric charges can have a physical significance. This work is intended to be a first step for the realization of an old idea of Einstein's (and also commented on by Dirac) to start with the electric charge, not with the Planck constant, as the primary concept for quantum theory.